How do you calculate equivalent units of production?

Process costing worked both ways, weighted average and FIFO, with the estimate that moves cost between profit and stock.

Julian R. Sterling · from Cost Accounting

Equivalent units convert partly finished work into the number of whole units it represents: units completed plus closing work in progress times its percentage of completion, separately for materials and for conversion cost. On an illustrative finishing process with 17,000 units completed and 3,000 in progress at 60 per cent, the weighted average method gives 20,000 equivalent units of materials and 18,800 of conversion, a cost of 31.00 a unit, and splits 597,200 of cost into 527,000 transferred out and 70,200 left in work in progress.

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When products flow continuously through a process, costs cannot be traced to individual jobs. They are collected for the period and divided by the output. The difficulty is that at the end of the month some of the output is half made. Equivalent units are how a half-made unit is counted as half a unit, and the counting has to be done separately for each cost that enters the process at a different stage.

The assumptions

One month in an illustrative finishing process.
Input	Units	Materials complete	Conversion complete
Opening work in progress	2,000	100%	40%
Started in the month	18,000
Completed and transferred out	17,000	100%	100%
Closing work in progress	3,000	100%	60%

Costs, in currency units.
Cost	Materials	Conversion	Total
In opening work in progress	24,000	9,800	33,800
Added in the month	216,000	347,400	563,400
To account for	240,000	357,200	597,200

Materials are added at the start of the process, so every unit in progress has all of its material. Conversion cost, labour and overhead, is added evenly as the work proceeds.

Step 1: equivalent units, weighted average

Equivalent units = units completed + closing WIP × % complete

Materials: 17,000 + 3,000 × 100% = 20,000. Conversion: 17,000 + 3,000 × 60% = 17,000 + 1,800 = 18,800.

Step 2: cost per equivalent unit

Cost per equivalent unit = (opening WIP cost + cost added) ÷ equivalent units

Materials: 240,000 ÷ 20,000 = 12.00. Conversion: 357,200 ÷ 18,800 = 19.00. A finished unit costs 31.00.

In Excel, with the conversion pool in C6, units completed in B4, closing units in B5 and the percentage in D5: =C6/(B4+B5*D5).

Step 3: assign the costs

Weighted average assignment.
Destination	Materials	Conversion	Total
Transferred out, 17,000 × 31.00			527,000
Closing WIP, 3,000 × 12.00 and 1,800 × 19.00	36,000	34,200	70,200
Accounted for			597,200

The total must equal the cost to account for, 597,200. If it does not, an equivalent unit count or a percentage is wrong. The 527,000 is the cost of goods moving to finished stock, which feeds cost of goods manufactured.

The FIFO alternative

The weighted average method blends last month's cost in opening work in progress with this month's. FIFO keeps them apart: it counts only the work done this month, and costs it at this month's prices.

FIFO equivalent units = completed − opening WIP × % already done + closing WIP × % complete

Materials: 17,000 − 2,000 + 3,000 = 18,000. Conversion: 17,000 − 2,000 × 40% + 1,800 = 18,000. Costs per unit: 216,000 ÷ 18,000 = 12.00 and 347,400 ÷ 18,000 = 19.30, so 31.30 a unit of this month's work.

Transferred out under FIFO is the opening work in progress, 33,800, plus 23,160 to finish it (1,200 equivalent units at 19.30), plus 15,000 units started and completed at 31.30, 469,500: 526,460 in all. Closing work in progress is 36,000 + 34,740 = 70,740. The total is the same 597,200; only 540 moves between finished goods and work in progress, because conversion cost rose from last month. FIFO shows that rise, 19.30 against 19.00; the weighted average dilutes it.

What if: the closing work is more or less complete

Weighted average, closing WIP 3,000 units, conversion stage varied.
Conversion complete	Equivalent units	Conversion per unit	Unit cost	Transferred out	Closing WIP
30%	17,900	19.96	31.96	543,240	53,960
60%	18,800	19.00	31.00	527,000	70,200
90%	19,700	18.13	30.13	512,244	84,956

The percentage of completion is an estimate, usually made by a supervisor on the last day of the month, and it moves cost between the income statement and the balance sheet. Between 30 and 90 per cent, about 31,000 of cost changes side. That is why the estimate should be documented and tested, not typed in.

The common mistake

Counting closing work in progress as whole units for conversion. Dividing 357,200 by 20,000 instead of 18,800 gives 17.86 of conversion a unit, values the closing work at 89,580 instead of 70,200, and understates the cost of goods transferred out by 19,380. The opposite error, forgetting that material is added at the start and applying 60 per cent to materials too, understates work in progress. Each cost needs its own percentage, set by when it enters the process.

Takeaway

Equivalent units are completed units plus closing work in progress times its stage of completion, cost by cost. Here they are 20,000 for materials and 18,800 for conversion, giving 31.00 a unit and a clean split of 597,200. Getting the unit cost right is the first half of the job; whether the overhead inside the conversion cost is assigned on the right driver is the subject of the free workbooks for Cost Accounting.

Questions readers ask

What is the difference between weighted average and FIFO equivalent units?

Weighted average counts all units completed plus closing work in progress, and divides opening and current costs together. FIFO deducts the work already done on opening inventory and divides current costs only. Here weighted average gives 18,800 conversion units at 19.00, FIFO 18,000 at 19.30; total cost of 597,200 is the same.

Why are equivalent units different for materials and conversion costs?

Because costs enter the process at different stages. Materials added at the start are 100 per cent complete in every unit in progress, so 3,000 units in progress are 3,000 equivalent units of material. Conversion cost added evenly is 60 per cent complete, so the same units are only 1,800 equivalent units of conversion.

What happens if work in progress is counted as whole units?

The cost per unit falls and work in progress is overvalued. Dividing 357,200 of conversion cost by 20,000 units instead of 18,800 gives 17.86 rather than 19.00, values closing work in progress at 89,580 instead of 70,200, and understates the cost transferred to finished goods by 19,380.

Read the whole case

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